Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dyn...Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.展开更多
We present results on approximate solutions to the biadditive equationf（x＋y,z-w）＋f（x-y,z＋w）=2f（x,z）-2f（y,w）on a restricted domain. The proof is based on a quite recent fixed point theorem in some function s...We present results on approximate solutions to the biadditive equationf（x＋y,z-w）＋f（x-y,z＋w）=2f（x,z）-2f（y,w）on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately （in some sense） must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.展开更多
In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps....In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.展开更多
The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group...The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.展开更多
文摘Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.
文摘We present results on approximate solutions to the biadditive equationf（x＋y,z-w）＋f（x-y,z＋w）=2f（x,z）-2f（y,w）on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately （in some sense） must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.
文摘In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.
文摘The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.
